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References (7)
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Manfred Schocker Mathematical Institute 24-29 St. Giles' Oxford OX1 3LB United Kingdom schocker@maths -
R. Carter (1985)
Finite groups of Lie type: Conjugacy classes and complex characters
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609303002868
- Publisher site
- See Article on Publisher Site
Abstract
Let (W, S be a finite Coxeter system, and let J⊆S. Any w∈W has a unique factorization w = wJ wJ, where wj belongs to the parabolic subgroup WJ generated by J, and wJ is of minimal length in the coset wWJ. It is shown here that wI = wJ if and only if wI = wJ, for all I, J ⊆ S. Furthermore, a similar symmetry property in arbitrary (WI, WJ‐double cosets is conjectured, which links this result to the Solomon descent algebra of W. 2000 Mathematics Subject Classification 20F55.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: May 1, 2004